IEOR162_HW1_Solution - IEOR 162 Spring 2009 Solution for Homework 1 2.1.2 y.50 0.10 x1 1 y =.30.70.30 x2 2.20.30.60 x3 y3 2.1.4 The ij'th element

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Unformatted text preview: IEOR 162, Spring 2009, Solution for Homework 1 2.1.2 y .50 0 .10 x1 1 y = .30 .70 .30 x2 2 .20 .30 .60 x3 y3 2.1.4 The ij'th element of (AB) = element ji of AB, = Scalar product of row j of A with column i of B. T Now element ij of BTAT = Scalar product of row i of BT with column j of AT = Scalar product of row j of A with column i of B. Thus, (AB)T = BTAT. 2.2.1 1 -1 4 1 - 1 4 2 1 x1 = 6 and 2 1 6 x 2 8 1 3 8 1 3 2.3.2 1 1 1 4 1 1 2 0 6 0 1 1 1 4 1 - 1 2 0 0 1 2 2 - 1 2 This system has an infinite number of solutions of the form x3 = k, x1 = 2 2k, x2 = 2 + k. 2.3.6 1 2 1 4 1 2 1 4 1 0 - 1 0 0 2 2 4 1 2 1 4 0 2 2 4 0 1 1 2 0 1 1 2 0 1 - 1 0 0 1 - 1 0 0 1 - 1 0 0 1 -1 0 1 0 - 1 0 0 1 1 2 0 0 - 2 - 2 1 0 - 1 0 1 0 0 1 0 1 1 2 0 1 1 2 0 0 1 1 0 0 1 1 1 0 0 1 0 1 0 1 0 0 1 1 Thus original system has a unique solution x1 = x2 = x3 = 1. ...
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This note was uploaded on 09/06/2009 for the course IEOR 162 taught by Professor Zhang during the Spring '07 term at University of California, Berkeley.

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